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34 changes: 17 additions & 17 deletions docs/model-structure.md
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Original file line number Diff line number Diff line change
Expand Up @@ -263,11 +263,11 @@ The change in the litter carbon pool over time is defined by the input of new li
and methane production:

\begin{equation}
\frac{dC_\text{litter}}{dt} = F^C_\text{litter} - F^C_{\text{decomp}} - F^C_\mathit{CH_4,litter}
\frac{dC_\text{litter}}{dt} = F^C_\text{litter} - F^C_{\text{decomp}} - F^C_{\text{CH}_4\text{,litter}}
\end{equation}

Where $F^C_\text{litter}$ is the carbon flux from aboveground plant biomass \eqref{eq:litter_flux},
$F^C_{\text{decomp}}$ is the total litter decomposition flux \eqref{eq:decomp_rate}, and $F^C_\mathit{CH_4,litter}$ is
$F^C_{\text{decomp}}$ is the total litter decomposition flux \eqref{eq:decomp_rate}, and $F^C_{\text{CH}_4\text{,litter}}$ is
the methane flux from the litter \eqref{eq:ch4}. Note that belowground turnover is routed directly to the soil carbon
pool (see Soil Carbon).

Expand Down Expand Up @@ -334,12 +334,12 @@ litter during decomposition, (ii) direct inputs from belowground plant turnover,
heterotrophic respiration and methane production:

\begin{equation}
\frac{dC_\text{soil}}{dt} = F^C_{\text{soil}} - R_{\text{soil}} - F^C_\mathit{CH_4,soil}
\frac{dC_\text{soil}}{dt} = F^C_{\text{soil}} - R_{\text{soil}} - F^C_{\text{CH}_4\text{,soil}}
\label{eq:Braswell_A3}
\end{equation}

where $F^C_{\text{soil}}$ is the total carbon input to the soil, $R_{\text{soil}}$ is the soil heterotrophic
respiration, and $F^C_\mathit{CH_4,soil}$ is the methane flux from the soil.
respiration, and $F^C_{\text{CH}_4\text{,soil}}$ is the methane flux from the soil.

This is equation (A3) from Braswell, et al. (2005), with the addition of the methane flux.

Expand Down Expand Up @@ -388,19 +388,19 @@ heterotrophic respiration is then defined as a fixed fraction of this decomposit
(\eqref{eq:decomp_carbon}--\eqref{eq:r_litter}), with the remainder transferred to the soil carbon pool
(\eqref{eq:soil_carbon}).

### Methane Production $(C \rightarrow CH_4)$
### Methane Production $(C \rightarrow \text{CH}_4)$

\begin{equation}
F^C_\mathit{CH_4,j} = K_{CH_4,j} \cdot C_\text{j} \cdot D_\mathrm{water, CH_4} \cdot D_\text{temp}
F^C_{\text{CH}_4\text{,}j} = K_{\text{CH}_4\text{,}j} \cdot C_\text{j} \cdot D_{\text{water,CH}_4} \cdot D_\text{temp}
\label{eq:ch4}
\end{equation}

\begin{equation*}
\small j \in \{\text{soil, litter}\}
\end{equation*}

The calculation of methane flux $(F^C_{CH_4})$ for soil and litter is analogous to that of $R_H$. It uses the same carbon pools as substrate
and temperature dependence but has specific rate parameters $(K_{\mathit{CH_4,}j})$, a moisture dependence function
The calculation of methane flux $(F^C_{\text{CH}_4})$ for soil and litter is analogous to that of $R_H$. It uses the same carbon pools as substrate
and temperature dependence but has specific rate parameters $(K_{\text{CH}_4\text{,}j})$, a moisture dependence function
based on oxygen availability \eqref{eq:water_ch4}, and no direct dependence on tillage.

## Carbon:Nitrogen Ratio Dynamics $(CN)$
Expand Down Expand Up @@ -530,7 +530,7 @@ and losses to volatilization, leaching, and plant uptake:
F^N_\text{litter,min} +
F^N_\text{soil,min} +
F^N_\text{fert,min} -
F^N_\mathrm{vol} -
F^N_\text{vol} -
F^N_\text{leach} -
F^N_\text{uptake}
\label{eq:mineral_n_dndt}
Expand Down Expand Up @@ -577,7 +577,7 @@ mineral nitrogen pool. The realized volatilization flux is proportional to $N_\t
soil moisture.

\begin{equation}
F^N_\mathrm{vol} = K_\text{vol} \cdot N_\text{min} \cdot D_{\text{temp}} \cdot D_{\text{water},N_{vol}}
F^N_\text{vol} = K_\text{vol} \cdot N_\text{min} \cdot D_{\text{temp}} \cdot D_{\text{water},N_\text{vol}}
\label{eq:n_vol}
\end{equation}

Expand Down Expand Up @@ -914,7 +914,7 @@ Where
- $W_{\text{WHC}}$: Soil water holding capacity

For moisture *dependency functions* (heterotrophic respiration, volatilization, and methanogenesis), SIPNET uses
$\mathrm{clip}(f_{\text{WHC}},0,1)$ internally. This prevents supersaturated water states from pushing moisture
$\operatorname{clip}(f_{\text{WHC}},0,1)$ internally. This prevents supersaturated water states from pushing moisture
response multipliers above their intended maxima.

#### Water Stress Factor
Expand Down Expand Up @@ -963,7 +963,7 @@ D_{\text{water},R_H} =

where $f_{\text{WHC}} = W_{\text{soil}} / W_{\text{WHC}}$ is the fraction of soil water holding capacity (soil water
divided by WHC), and $b$ is the soil respiration moisture effect exponent. In implementation, this term is evaluated as
$\left(\mathrm{clip}(f_{\text{WHC}},0,1)\right)^b$ when moisture dependency is active.
$\left(\operatorname{clip}(f_{\text{WHC}},0,1)\right)^b$ when moisture dependency is active.

If the command-line option `ANAEROBIC` is on, the dependency is represented as a partition
between aerobic and anaerobic pathways:
Expand All @@ -975,7 +975,7 @@ D_{\text{water},R_H} = (1 - A) D_\text{aer} + \eta A

where $\eta \in (0, 1]$ is the relative anaerobic decomposition rate.

#### Nitrogen Volatilization Moisture Dependence $D_{\text{water},N_vol}$
#### Nitrogen Volatilization Moisture Dependence $D_{\text{water},N_\text{vol}}$

The volatilized nitrogen flux (treated as N2O-dominated in the absence of explicit speciation) is assumed to peak at
intermediate redox conditions, where aerobic and anaerobic processes overlap:
Expand All @@ -985,18 +985,18 @@ D_{\text{water},N_{vol}} = 0.05 + 3.8 A (1-A)
\label{eq:water_nvol}
\end{equation}

where 0.05 represents baseline aerobic volatilization and the factor 3.8 scales the quadratic term so that the maximum value is 1, and $D_{\mathrm{water},N_{vol}} \in [0.05, 1]$.
where 0.05 represents baseline aerobic volatilization and the factor 3.8 scales the quadratic term so that the maximum value is 1, and $D_{\text{water},N_\text{vol}} \in [0.05, 1]$.

#### Methane Production Moisture Dependence $D_{\text{water},CH_4}$
#### Methane Production Moisture Dependence $D_{\text{water},\text{CH}_4}$

\begin{equation}
D_{\text{water},CH_4} = A^p
D_{\text{water},\text{CH}_4} = A^p
\label{eq:water_ch4}
\end{equation}

where $p \ge 1$ controls the sharpness of the anaerobic transition.

This represents a collapsed redox ladder (i.e., $CH_4$ production once alternative electron acceptors are depleted),
This represents a collapsed redox ladder (i.e., $\text{CH}_4$ production once alternative electron acceptors are depleted),
without explicit electron-acceptor pools.

## Agronomic Management Events
Expand Down
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